Array pre-processing for the SESAM system: DOA Mean Square Minimization

Authors:

  • Hyberg Per

Publish date: 2004-01-01

Report number: FOI-R--1297--SE

Pages: 25

Written in: English

Abstract

This report treats interpolation (mapping) of the output vector from an existing antenna array onto the output vector of another (virtual) array when the signal directions of arrival (DOAs) are known only to within a wide sector. In an earlier companion paper a first order condition for zero DOA bias under such mapping was derived, and also used to construct a design algorithm for the mapping matrix that minimized the DOA estimate bias. This bias minimizing theory is now extended to minimize not only bias, but DOA mean square error (MSE), i.e. bias squared plus variance. We first derive an analytical expression for mapped DOA MSE. Thereafter we propose a design algorithm for the transformation matrix that generates mapping errors minimizing this MSE. Generally, DOA MSE is not reduced by minimizing the size of the mapping errors, but instead by rotating these errors and the associated noise subspace into optimal directions relative to a certain gradient of the DOA estimator cost function. The analytical MSE expression and the design algorithm are supported by simulations that show not only conspicuous MSE improvements in relevant scenarios, but also a resulting pre-processing of better robustness for low SNRs as compared to the pure bias minimizing design described in the earlier paper.

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